Uncertainty Visualization of the Marching Squares and Marching Cubes Topology Cases

TL;DR

This paper introduces methods to visualize and quantify topological uncertainty in Marching Squares and Marching Cubes algorithms when applied to uncertain scalar field data, aiding better interpretation of complex data structures.

Contribution

It proposes topology case count and entropy-based techniques for uncertainty quantification in MS and MC algorithms under various uncertainty models.

Findings

Effective visualization of topological uncertainty using color mapping and entropy isosurfaces.

Techniques applicable to both independent and correlated uncertainty models.

Demonstrated utility on synthetic and real datasets.

Abstract

Marching squares (MS) and marching cubes (MC) are widely used algorithms for level-set visualization of scientific data. In this paper, we address the challenge of uncertainty visualization of the topology cases of the MS and MC algorithms for uncertain scalar field data sampled on a uniform grid. The visualization of the MS and MC topology cases for uncertain data is challenging due to their exponential nature and the possibility of multiple topology cases per cell of a grid. We propose the topology case count and entropy-based techniques for quantifying uncertainty in the topology cases of the MS and MC algorithms when noise in data is modeled with probability distributions. We demonstrate the applicability of our techniques for independent and correlated uncertainty assumptions. We visualize the quantified topological uncertainty via color mapping proportional to uncertainty, as well as with interactive probability queries in the MS case and entropy isosurfaces in the MC case. We demonstrate the utility of our uncertainty quantification framework in identifying the isovalues exhibiting relatively high topological uncertainty. We illustrate the effectiveness of our techniques via results on synthetic, simulation, and hixel datasets.